# Real Numbers Worksheet

MAP
Mathematics Achievement Program
SFSU – High School Collaborative
TOPIC 3: Real Numbers
Real numbers can be represented by points on a number line. Each real number
corresponds to a point on the number line, and each point on the line corresponds to a real
number. Some important subsets of real numbers are: integers, which are the numbers
{
}
K
K
in the set
,
, 2
1
0 ,
, 1 ,
, 2
; fractions (also called rational numbers), which are
a
numbers of the form
, where a and b are integers and b ? 0; and irrational numbers,
b
which are numbers that cannot be written as fractions.
A square root of a real number a, written
a , is a real number n whose square is
n =
2
a; that is,
a = n when
a
.
=
2
Example 1:
There are two square roots of 16, 4 and – 4, because
4
16
and
( )
=
16 = , and
2
. Four is the positive square root of 16, written
4
4
16
=
– 4 is the negative square root of 16, written
16
4
.
Recall that the square of any real number is either zero or positive. Therefore
only nonnegative real numbers have square roots; negative numbers do not have real-
number square roots. For example,
16
is not a real number because there is no real
number whose square is –16.
A perfect square is a number in the set {0, 1, 4, 9, 16, 25, …}. We can use
perfect squares to approximate square roots.
Example 2:
Approximate
17 without using a calculator.
Because 17 is between the perfect squares 16 and 25,
17 is between
16 and
25 . Therefore,
17 is between 4 and 5.
________________________________________________________________________
1. List the perfect squares less than 150.
For exercises 2-5, use perfect squares to approximate the square root without using a
calculator.
2.
7
3.
31
4.
85
5. 128
________________________________________________________________________
The absolute value of a real number a, written a , is the distance from 0 to a on
the number line. The absolute value of a real number is never negative (Why?).
________________________________________________________________________
For exercises 6-11, find the absolute value.
6.
5
7. 12
8.
12
− −
9.
5
10. 2 5
11. 5 2
8